David Cameron was accused of revealing his ill-suppressed Bullingdon Club instincts when he shouted at the Labour frontbencher Angela Eagle to "calm down, dear" as she berated him for misleading MPs at prime minister's questions.

Within minutes, Labour accused him of being "sexist, patronising, insulting and un-prime ministerial". The Labour deputy leader, Harriet Harman, called for an apology, and a spokesman for the Liberal Democrats – increasingly eager to show they are locked in a loveless marriage with Cameron – said: "We would not have used that language."

Eagle, writing in the Guardian, said it was "a phrase that no modern man would use towards a woman.

"It reminds me of none other than Flashman, the appalling bully in Tom Brown's Schooldays. Flashman's increasingly frequent appearances at Westminster are now being remarked upon even by MPs in his own party."

Downing Street claimed Labour had suffered a sense of humour failure and Cameron was merely using a catchphrase uttered by film director Michael Winner in an insurance advert.

In a rapid damage limitation operation, Cameron's spin doctors said he had used the phrase before, as leader of the opposition, in remarks aimed either at Gordon Brown or David Miliband.

Cameron oscillates at prime minister's questions between showing great courtesy to backbench MPs and suddenly displaying a fierce temper, for instance describing Ed Balls last month as one of the most annoying politicians in Westminster.

Balls himself said after prime minister's questions: "If I had ever said 'calm down, dear' to Yvette [Cooper, the Sshadow home secretary] at home, she'd have clocked me one."

Likeability and modernity are two of Cameron's strongest suits, and his aides have told him before to rein back on anything that smacks of posh boy pugilism.

The row broke out as he was forced on to the defensive over his troubled health reforms. Eagle picked him up when he started to claim that a former Labour MP who supports the health reforms, Dr Howard Stoate, had been defeated at the election by the Tories.

Eagle shouted that Stoate had stood down before the election and the PM had got his facts wrong. Cameron told the shadow chief secretary to the Treasury to "calm down, dear, and listen to the doctor". Chancellor George Osborne laughed his head off, while Nick Clegg, sitting on Cameron's other side, looked non-plussed. Cameron repeated the phrase five times.

Winner sprung to Cameron's defence: "I find it unbelievable that Harriet Harman, the deputy leader of a supposedly important party, sees fit to go on about my phrase 'calm down, dear'.

"Which planet is Miss Harman on? Does she not know that this phrase, which I created 10 years ago, has become a part of the nation's language?

"It's used by everybody. All classes of people shout it at me, truck drivers, builders, posh people, they come over in restaurants, it's a bit of fun, Labour should get a sense of humour. Fun is fun, and please don't try and stop people having fun, things are dour enough as it is."

Winner coined the phrase for his friend Peter Wood who formed the internet insurance company esure back in 2001.

Eagle said: "I have been patronised by better people than the prime minister ... It is for the prime minister to decide whether he expressed himself appropriately in the Commons.

"It is up to him as to whether he wants to annoy 51% of the population."

She said he should apologise first for the state of the economy'

The prime minister's spokeswoman said: "Let's not over-analyse it; it was a humorous remark. Mr Cameron was clearly mimicking a popular TV ad. No offence was intended."

But Danny Alexander, the Treasury chief secretary, was less insouciant saying " Obviously, if something has caused offence, obviously that was not right. I hope it has not caused offence, because it was a joke".

But before journalism gets on its high horse over sexism, look too at the Telegraph website where the assistant comment editor Lucy Jones posted a picture of Labour MPs behind Ed Miliband at prime ministers questions and asking the question "Who is this busty lass?" with a red ring round the chest of one Labour MP. Read and quickly despair.